I'd take a repair kit instead of a medkit - you already have a first aid kit, and will mostly be in ship combat.

As for the rest
Laser has more ammo, cheaper
Particle gun has infinite ammo, less powerful
Electrolaser does little damage but disables electronics, so it's more like a paralysis beam
Railgun does the most damage but has less ammo and is more expensive.

Of course, if you take a 2 cred weapon you can buy a 1 cred thing as well, if you like. Either option has merit.

I'll take suggestions on weapons, but I'm kind of thinking of using telekinetic powers offensively as ship weapons.

Name: TrontosAge: 31Gender: MalePersonal Information: With a muscular and tall build, Trontos originated from one of the lesser known worlds within the galactic plain. In his late teens he took a transport off world in order to learn the ways of an ancient order known as the Syth. Over the years he became obsessed with Syth teaching, using them to train himself into becoming proficient in the art of assassination. Has been in cryo for 300 yearsPersonality: Speaks in old English when furious, very territorial, tries to intimidate target prior to attacking.Reason your character got REKT: Was blackmailed by a client who reported the murder to the REKT team which quickly imprisoned Trontos for the murders of several high profile individuals. Stats:Energy:0Durability:0Maneuverability:1Hacking:-2Computer:-1PSI Unit:1Robotics:0Engines:0Skills:Charisma:0Intuition:1Handiwork:0Conventional:-1Unconventional:1Exotics:-2General Knowledge:0Auxiliary:0

Your stats/skills/loadout are all valid, so that's good. You can use all the gear you listed. Interesting choice, not getting exotic ability.

You can't use most weaponry. This is inadvisable. You don't have any other methods of aggression, either. I would suggest putting a point into unconventional from intuition/general knowledge, or getting a point in exotics.

As Dino pointed out, you can still choose one more amp. Without exotics, your only choice is the telepathic amp unit. (Note: Neither of the amp units you are capable of choosing are actually capable of causing damage.)

If you decide to go with unconventional, you may as well get a sword or something explosive. I hear there's a nice lightsaber-like sword your character might be interested in.

I notice you didn't spend any creds... and I think I can see why. With your current set of stats/skills, you can't get any ship weapons, either. You really might want to think about fixing that, if you don't want to be a Francis.

Name: Gene "Spark" Weber, Jr.Age: 27Gender: MalePersonal Information: Gene was born into a prominent family of military men on New Earth. While his parents wanted him to enroll in military school and eventually enlist in the United Galactic Military, like most young men of the Weber family had, Gene began to take a liking to computer science at an early age - much to the dismay of his parents. He turned out to have quite a knack for it, and under pressure from his family, he decided to enlist in the Galactic Military as an electronic warfare specialist.
Gene's training career in the Galactic Military was an otherwise unremarkable one; his superiors and instructors, however, did not view him highly, as he was quite introverted and thus not a 'team player' in any sense of the phrase.
His career came to an end when he was court-martialed shortly after a failed operation in the field, killing everybody in his squad but himself. It was later revealed that he had failed to communicate with the rest of his squad, and they walked into a trap that he was supposed to disarm.

Gene stands about 178 centimeters (5' 10") tall; he is quite strong, has well-toned muscles from his service in the Galactic Military, but he is not very bulky. He sports brown hair and light blue eyes. A scar runs down the upper part of his left arm, from an accident during his military career involving a frag grenade.Personality: Gene is introverted; he dislikes communication, and prefers to work alone. His withdrawn personality primarily stems from his childhood, when he was ruthlessly bullied for pursuing a career computer science instead of the military.

While Gene does not care much for group activities, he puts up with it, considering it to be a chore. He makes attempts to converse with others in his group, but will often speak without much tact or forethought.Reason your character got REKT: Gene was court-martialed for gross negligence in carrying out an operation, and was given the choice to be dishonorably discharged or be shipped to Tartarus' ReKT in a cryogenic coffin. He took the easy way out - he just couldn't bear to see his family's ashamed faces upon learning he'd been dishonorably discharged, so he signed the transfer papers. The very next day, he was unceremoniously chucked inside his coffin and sent on his way to Tartarus.Stats:Energy:1Durability:1Maneuverability:0Hacking:1Computer:0PSI Unit:-2Robotics:-2Engines:-2Skills:Charisma:-2Intuition:0Handiwork:1Conventional:1Unconventional:0Exotics:-2General Knowledge:-2Auxiliary:1

Name: Felicity "Felix" WalkerAge: 19, though she is often mistaken to be 25Gender: FemalePersonal Information: Twelve cold years ago, the little girl tiptoed around her house, wrapped in a blanket awoken by a nightmare. The air was still but peaceful; everything except her dream seemed to be in place. She proceeded to her parent's room, pushing the creaking door a little, just to take a peek. And there he stood, tall and strong, his bare muscles illuminated by the pale moonlight. He held an old dagger, creeping up behind her mother. With a dozen stabs he rendered her lifeless, feeling her crimson blood on the blade's edge. The girl dropped her blanket, just staring at her father. His dark eyes stared back at her. He reached out to his daughter but she just stepped back, not shifting her gaze from him. She kept backing away, unaware of the flight of stairs behind her. A little slip and she fell hard on her head. A scar through her right eyebrow split her beautiful skin. Her memory vanished as quickly as her father.

She was sent to an orphanage, her memory wiped out a second time so that she would not remember the slightest fragments of her dark past. Growing up over there for the next three years, rumours spread about the incident. Her temper was uncontrollable and curiosity out of hand. She broke out to see the world and discover her true identity.

Felicity adopted the name "Felix" to keep her identity as a girl a secret so that she could get along with any bounty hunters along the way, whom she could help and in return seek vengeance for her mother's death.

Shoulder-length (could say medium height) black hair with red and pink highlights. Golden brown skin with many cuts and bruises, most notably the scar through her right eyebrow; alright looking, not anything spectacular. Short-ish at 5'6". Has a bit of muscle due to the fact that she has been running around, falling in trouble, trying to figure out her past.Personality: Aggressive but has a soft side for the people she likes. Usually has enough patience to be tolerant towards you but if you make her angry, she'll turn into a demon. Tends to be diplomatic and persuasive to get her way if necessary. Will go out of the way to get what she wants. Usually tries to keep her identity a secret because many want to get rid of her. She is also very fickle. What empowers her is her desire to know more and to be loved.Reason your character got REKT: A bounty hunter, annoyed by the competition with her and her boss decides to capture her and send her away. Enough money to do the job.Stats:Energy:1Durability:0Maneuverability:0Hacking:1Computer:0PSI Unit:-1Robotics:0Engines:-2Skills:Charisma:1Intuition:0Handiwork:0Conventional:0Unconventional:1Exotics:-1General Knowledge:0Auxiliary:-2

What was your character's dream, before getting shipped to Tartarus? Was there anything in particular your character dreamed of accomplishing someday?
On one hand, Felix wants to know more about her past and avenge the death of her mother while on the other she dreams of being a good bounty hunter herself, with enough people to trust. She also dreams of time travel so that she could change the past.

List a few ways your character's personality could develop and/or change over the course of the story.
When with someone who truly cares about her and understands her, she could evolve into a more patient and peaceful person. When with someone fishy, even the littlest of things will annoy her. Her fickle nature could set her off.

What really sets your character apart from other characters, and makes your character unique?
She tries to keep her distance from others at times but sometimes she might cling on to them if she trusts them. The desire to know more and to be loved burns within her.

What's a serious flaw your character has, that he/she has difficulty overcoming even when it matters most? Feel free to list more than one.
She cannot bear any insult against her family, especially her mother. She is quite clingy and protective of those she loves. Sometimes she dislikes the fact that she is female and hides this.

Does your character have any interests? Hobbies? Passions or strong opinions? Relate two or more of these.
Felix loves archery and anything that involves violence and a show of strength, although she's not always good at it. She enjoys coding and manipulating anything digital to favor her chances, even if it's just to play a prank on her friends. She is quite good at seducing others, which she does if nothing else works out.

Tell a short story about something that happened between your character and someone they were close to before they got shipped to Tartarus.
Felix was kidnapped by an enemy bounty hunter whom she sweet-talked to twice before. He fell for it both times but this time he managed to kidnap her and send her away before her team got the loot. Her boss, was not in very good terms with her and only cared about the money which is one reason why no one came back for her. She doesn't have any friends.

Tell a short story about a scenario where your character is forced to leave an ally behind to finish the mission.
Felix would never ever leave anyone behind. If she has to, she would volunteer to stay back.

Tell a short story about a scenario where your character dies in what he/she would consider the best way possible.
She would accept death only when after quest for revenge and tying up all the loose ends. If it's inevitable, she would prefer to die a painless, quit death, like a bullet to the head.

Tell a short story about a scenario where your character would be in his/her element.
On missions where she has to exterminate everyone on board or a stealth mission, she performs her best. When it comes to a situation where she has no weapons, she resorts to striking a truce, which she often breaks when she gets what she wants.

Tell a short story about a scenario where your character is forced to make a difficult decision.
Choosing whom to save among her loved ones. Being insulted.

Few remarks:
-having 1 energy and 0 conventional, and 1 unconventional and 0 maneuverability, will make stuff a tad harder early on, and you'll need to pick a good loadout. However, it well give you more flexibility later on, so it's not a bad thing, just something to be wary off.
For infantry loadout, there are a few unconventional weapons that roll energy and unconventional and are thus great for that build. (Kinetic gauntlet, plasma baton, plasma bomb launcher)
Also 2 that only use unconventional (gravity gun, nanobot globule)
For ship, there's only really the REAPER, but that would cost all your money so might not be ideal, depending on how much ship and infantry combat there is in your first mission.
-you mention stealth, but stealth uses speed (= engines) and maneuverability, so you suck at stealth right now.
-While psi can be sometimes useful for non-psi characters (it's also willpower), exotic isn't really, so I'd put the -2 there instead of in auxiliary.
(Which also determines your ability to improvise)

Dino's analysis was good - you should probably move a point to either maneuverability or unconventional, or you're going to be really hampered early on. The reason for this is that many things roll two stats. Swords, for example, roll maneuverability and unconventional. Assault rifles roll Energy (strength, on foot) and conventional. The way they give bonuses is by dividing their sum by 2, and rounding down. If you don't have at least +1 in both, you might as well not have put any points into it at all, because you won't get a bonus to your roll. Two zeroes is a 33% base chance to succeed. You'll probably want to be either exceedingly clever, or raise that to 50% with 1,1. (Or, 67% with 2,2. Alternatively, 0,2 would give the same effect as 1,1 as well - 50% base chance to succeed.) Note: this is just a suggestion, and you're free to ignore.

Next, given the timeline in your post, you may have missed the part where everyone has been in cryo for an undetermined period of time - somewhere between 5 and 90 years, if I remember right. This is not something that normally happens - in fact, even on the Nemesis, nobody knew cryo tech existed. Someone up-top was conducting experiments to try to get cryo tech to actually work, and nobody - not even SCAMPS - was let in on it. The "why" of this remains to be seen. The cryo tech you got put to sleep with has only a 25% success rate for awakening (so far), which makes you fairly lucky to be alive.

And that's it! You could post your character as-is if you want.

((Also, for posterity, going to mention that we gave TotallyNotHuman advice on his character in IRC instead of here, because that was more convenient.))

Explanation:
For the stats, a combination of PSI and unconventional. But in such a way you can actually use your PSI weapons. Not much point in putting points in PSI and blocking you from actually using it by putting -2 in exotic as nearly all PSI weapons roll exotic or require it for you to be allowed to use them.
(See: the microwave amp you added you can't use because it requires at least 0 exotic)
What you sacrifice for this - handiwork I set to -2. We have plenty of medics, so no big deal. Intuition starts at 0, you can level it after the first mission.

Grav amp: force moving things. Alternatively Mass mamipulation amp
After levelling PSI and charisma you can also get a charisma amp for "these aren't the droids you're looking for". Not on your first mission though.
Armor: In a melee build, this can help
Blunderbuss: you need something for you ship